European Patent Application EP-0 323 668, which corresponds to U.S. Pat. No. 4,893,283, describes an apparatus of this kind in which an interesting compromise is realised between the rate of operation and the resolution. The described solution consists in the successive emission, be it as closely successive as possible, of m focused ultrasonic beams in m different directions, the reception and processing of the echographic signals formed being provided by known means for simultaneously focusing the m ultrasonic beams from said m directions (these known means are described, for example in the article by O. T. von Ram, S. W. Smith and H. E. Pavy "High-speed ultrasound volumetric imaging system, part II: Parallel processing and image display", IEEE Trans. on UFFC, Vol. 38, No. 2, March 1991, pp. 109-115). However, using this apparatus it is necessary to wait until all successive emissions have been completed before the reception of the echographic signals retumed to the transducers may commence (this emission sequence has a duration equal to the sum of the maximum delay times corresponding to each focusing rule for the emitted beams). Actually, it is impossible to emit and receive simultaneously by means of a transducer. These restrictions in respect of time on the one hand limit the number of beams to be emitted and on the other hand lead to the exclusion of a given object thickness from the zone to be scanned, which thickness constitutes a kind of dead zone corresponding to the part of the object situated nearest to the transducer array.